On the structure of the Witt group of braided fusion categories

Academic Article


  • We analyze the structure of the Witt group W of braided fusion categories introduced in the previous paper arXiv:1009.2117v2. We define a "super" version of the categorical Witt group, namely, the group sW of slightly degenerate braided fusion categories. We prove that sW is a direct sum of the classical part, an elementary Abelian 2-group, and a free Abelian group. Furthermore, we show that the kernel of the canonical homomorphism S: W --> sW is generated by Ising categories and is isomorphic to Z/16Z. Finally, we give a complete description of etale algebras in tensor products of braided fusion categories.
  • Authors

  • Davydov, Alexei
  • Nikshych, Dmitri
  • Ostrik, Victor
  • Status

    Publication Date

  • March 2013
  • Has Subject Area

    Published In


  • Braided tensor category
  • Etale algebra
  • Witt group
  • Digital Object Identifier (doi)

    Start Page

  • 237
  • End Page

  • 269
  • Volume

  • 19
  • Issue

  • 1